Sum of Triangular Numbers II (visual proof via cannonballs)

Описание: This is a short, animated visual proof showing how a formula for the sum of the first n triangular numbers (which themselves are sums of the first n integers) using a three dimensional stack of spheres (that look like cannonballs). #manim #math #mathvideo #mathshorts #sequences #triangles #animation #theorem #pww #proofwithoutwords #visualproof #proof #triangularnumbers #sums #pww​ #proofwithoutwords​ ​ #proof​ #algebra #finitesums #mathematics​ #mathvideo​ #mtbos

Here is an alternate video for a related sum:
   • Sum of Triangular Numbers I (visual proof)  

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This animation is based on a visual proof by Deanna B. Haunsperger and Stephen F. Kennedy from the February 1997 issue of Mathematics Magazine (https://www.jstor.org/stable/2691052) page 46.

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Music in this video:
Sunrise at the White Citadel by Justin Allan Arnold | https://www.ifnessfreemusic.com
Music promoted by https://www.free-stock-music.com
Attribution 4.0 International (CC BY 4.0)
https://creativecommons.org/licenses/...